7. Conclusion

After defining the approximate arithmetic (floating-point arithmetic) of computers and showing the consequences of this arithmetic at the level of each elementary arithmetic operation, we presented various deterministic and probabilistic approaches to estimating the propagation of rounding errors in scientific computing.

We have also proposed a method for evaluating the influence of data uncertainties on calculation results. In the field of deterministic approaches, we have presented the regressive analysis of rounding errors, also known as a posteriori analysis, by J.H. Wilkinson, as well as a formalized error analysis scheme by F.W. Olver, and considered methods based on interval arithmetic.

The essence of regression analysis is to consider that any computer result resulting from an ordered sequence of calculations performed on data is...